Many signal processing problems require flexible real-time implementations of linear signal processing operations such as Fourier transforms, convolution, correlation, and beamforming. All of these operations may be performed at high throughput rates using the discrete Fourier transform (DFT) implemented via the chirp-Z transform (CZT) algorithm with a transversal filter or cross-convolver used to perform the required convolution or correlation with a discrete chirp. Special purpose methods have also been described in the prior art for combining a number of CZT modules to perform a longer DFT. The prior art methods, however, required a different acoustic surface wave filter for each different number of CZT modules to be combined. This limits the flexibility of the transform size attainable with a given set of components, and also prevents the longer transform system from being externally clocked, since the propagation time through the surface wave device cannot be varied by more than a small fraction of one percent.